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Unformatted text preview: Circle instructor: Poduska or Morrow 1 Name: 90 LVNWV" '
Lab period: Student Number: MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF PHYSICS AND PHYSICAL OCEANOGRAPHY Physics 1051 Winter 2009 Term Test 2 March 20, 2009 INSTRUCTIONS: 1. 2. 3. Do all questions. Marks are indicated in the left margin. Budget time accordingly.
Write your name and student number on each page. You may use a calculator. All other aids are prohibited.
Write answers neatly in space provided. If necessary, continue onto the back of the page. Do not erase or use “whiteout” to correct answers. Draw a line neatly through material to
be replaced and continue with correction. Assume all information given is accurate to 3 signiﬁcant ﬁgures. Don’t panic. If something isn’t clear, ASK! SEE LAST PAGE FOR SOME POTENTIALLY USEFUL
FORMULAE AND CONSTANTS For ofﬁce use onl : Circle instructor: Poduska or Morrow 2 Name:
Lab period: Student Number: [10] 1. The graph below shows equipotential lines around three point charges; A, B, C, and D.
The lines are drawn in steps of 20 V for all voltages between 60 V and +60 V. The
electric potential is taken to be 0 at inﬁnity. y(cm) (a) What is the sign of charge A? Which other charge has the same sign?
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c H meat: c #493 war/mu; (b) Carefully draw the electric ﬁeld line that starts on one charge, passes
through point k, and ends on another charge. Be sure that the direction of the ﬁeld line and the charges on which it starts and ends are clearly shown.
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[09 Mo nan/m; Alli/is” ﬁr mass/1w: . , [Mam/c FIELD zwf 57,72 r; 04/ Parr/Vi, twp; DIVA/1517114?  (c) Is the magnitude of the electric ﬁeld larger at point e or at point f? Brieﬂy
explain your choice. — Ewe aw an /E/ML 1’.
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S"WM/er" hear @ ,IZM 1726!” P /£/‘ Agog So swaﬂér A0? i‘a/Ip/I‘es #0470.» /f/ (d) Using the scale on the xaxis and the equipotentials, estimate the magnitude of the electric ﬁeld at point e. /f€/:4L/ : RQV’ [’JOV): 4,4454%”: 447FO/ﬂ7‘ 5‘1, 0“]0/1 (6) How much work is done by the electric ﬁeld as an electron is moved from
point h to point 9? (hint: be careful with the sign) ,
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due it (Jet/[Vii /" Circle instructor: Poduska or Morrow 3 Name:
Lab period: Student Number: [10] 2. (a) A cavity within an uncharged conducting object contains a point charge
q = —5.0x10‘15 C as shown. (i) What is the total ﬂux through a spherical closed surface a that
is embedded entirely within the conducting material? H
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a (ii) What is the magnitude of the total ﬂux through a spherical closed surface b
that entirely encloses the conducting object? Canada» An; no ”cf 0144/7! go (La/7? C'Mé/ﬂfé/gy 5" «5300 6'
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A/,'”7 (iii) What is the total charge on the outside surface of the conductor?
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SUM/ace /¢0n/dc/£w ”ms/‘56 +5 5 “fax/o ”/rC Gaussian (b) The ﬁgure to the right shows a portion of an inﬁnite, uniform sheet
/’ surface of charge (positive). A cylindrical Gaussian surface with a cross
sectional area A = 0.03 m2 is drawn on the sheet. The electric ﬂux
through the top surface of the cylinder is 15.0 N  m2 / C . a (i) What is the magnitude of the electric ﬁeld at a point 2.0 cm above the surface ofthe sheet?
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(ii) What is the total ﬂux through the closed cylindrical Gaussian surface drawn
on the ﬁgure? [f ”j;
£594“ I‘M, Gaza“ 1444 Cf “J! ’A) Wm» '7 @50/‘4’01 pa?! addwﬂa&)“ ¢ mm; : rap ‘ difomw (aw/min s/LQ' : 0) (iii) What is the charge per unit area, 0' , on the sheet? @% :6W%  z ,y 2
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0 Circle instructor: Poduska or Morrow 4 Name:
Lab period: Student Number: [10] 3. A uniform magnetic ﬁeld of 13 T is directed into the page as shown. Two oppositely charged plates, Cl and b, are separated by 2.5 mm and located so that the uniform electric
ﬁeld between them is perpendicular to the magnetic ﬁeld. While it is between the charged plates, an ion with a charge of +e (1.6 X 10'19 C), a mass of 1.6 x10"25 kg and a
speed of 3.0 x104 m/s travels in a straight line without being deﬂected. (a) What is the electric ﬁeld in the region between the plates? Give your answer in unit
vector notation. (b) What is the potential difference, V}, — V; , y
between the charged plates? T (0) Beyond point e on the ion’s path, there is no
electric ﬁeld and its motion is only affected by the . . . ..
uniform magnetic ﬁeld. What is the magnitude of T x x X xx x . . . . 2.5mm @» __.x
the centripetal force on the 1011 after it passes pomt i xv=3.0))é10‘ m)/<s Cx \‘x x
c? Is its path clockwise or counterclockwise? b . “.
x x x x x x (d) What is the radius of the ion’s path once it is
beyond point c and affected only by the uniform X X X X X X
magnetic ﬁeld? (a) pﬂr‘ far/("if E Marc 1‘” a §/"GI‘9/¢f /m£3 ézve A
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Lab period: Student Number: [10] 4. A uniformly charged ring of radius a is located with its centre at the origin such that
the plane of the ring is perpendicular to the xaxis. (a) If the total charge on the ring is Q, how much charge, dq, is found on the very
small ring segment of length ds, as shown? (b) What is the contribution to the electric potential at point P from the charge in
segment ds? Assume V = 0 at inﬁnity. (c) Starting from V = ke J41 , ﬁnd an expression for the electric potential at point P
r due to the entire ring. ((1) What is the electric potential at the origin due to the entire
ring? V
l
i (e) Assume that the radius of the ring is a = 2.5 cm and that
the total charge on the ring is Q = 6.O><10'12 C . How
much work is done by the electric ﬁeld if a particle with a
charge of q = —3.2 XlO'19 C is moved from the origin to
point P at L = 9.0 cm ? (W566; DEXQ 3110!
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//\V\« ar/‘7M 5 P S‘o Lv’ 1‘s ne7aﬁw) , ,4, dap/ndﬂrﬁ Circle instructor: Poduska or Morrow 6 Name:
Lab period: Student Number: Some Potentially Useful Formulae and Constants: E2=ke qlgz £12 qq
r U12=ke 1 2
"12
E=kei2r‘
r 3»
AU=—q[Ecz§
—* q. A
E=keZ—‘3 3»
in AV=VB—VA=—jEd§
A
~ qu
E=k ————r —
eJrz AU—qAV
CDE=JE'dA E=_ d_V;+d_V;+ﬂk
dx dy dz
qinside
(I)
E 60 R=M
I
V=hg
r F3=q17x§
V=kezi v2
1' ri (Ir:—
r
Vzke ﬂ 4 3
r Vsphere=37rr
C circle = 27rr (circumference) 2
Asphere=4ﬂr
A =7rr2 circle Physical constants: k = 1 =899x109Nm2/C2 e=1.602><10‘19 c
e 47:30 '
go =8.85x10'12 C2 /Nm2 me =9.11x10’31 kg Mathematical formulae: in; I__d_x_=_i__
r2 _ r (x2+y2)m y2 x2 +y2
Iii—x—zlnx J‘ xdx 2— 1 x (x2+y2)m x2 +y2 NW 1n[x+m] —y A  E = ABcosa = AxBx + AyBy + A2132 21x1”; = (/1sz #1sz )2 +(Asz —Asz)]'+(AxBy —AyBx)12 ...
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 Winter '12
 MichaelMorrow

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